Undergraduate Programme and Module Handbook 2018-2019 (archived)

# Module MATH4041: PARTIAL DIFFERENTIAL EQUATIONS IV

## Department: Mathematical Sciences

### MATH4041: PARTIAL DIFFERENTIAL EQUATIONS IV

Type | Open | Level | 4 | Credits | 20 | Availability | Available in 2018/19 | Module Cap | Location | Durham |
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#### Prerequisites

- Analysis in Many Variables II (MATH2031) AND other Mathematics modules to the value of 80 credits in Years 2 and 3, with at least 40 credits at Level 3

#### Corequisites

- None.

#### Excluded Combination of Modules

- Partial Differential Equations III (MATH3291)

#### Aims

- To develop an understanding of the theory and methods of solution for Partial Differential Equations.

#### Content

- First order equations and characteristics.Conservation laws and their weak solutions.
- Systems of first-order equations and Riemann invariants.
- Hyperbolic systems and their weak solutions
- Classification of general second order PDEs
- Poisson,Laplace, Heat and Wave equations:existence and properties of solutions
- Reading material on one of the following topics: applications of PDEs, further theory of PDEs

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will:
- be able to solve problems in Partial Differential Equations;
- have an understanding of theoretical mathematics in the field of Partial Differential Equations;
- have mastered a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas:
- Solution of first order equations and systems.
- Classification of second order PDEs, and their solutions.
- have an advanced understanding in one of the following areas: applications of PDEs, further theory of PDEs

Subject-specific Skills:

- Students will have highly specialised and advanced mathematical skills in the following areas: Modelling and Analysis of PDEs

Key Skills:

- Students will have an appreciation of important Partial Differential Equations and their fundamental properties.
- Students will be able to study independently to further their knowledge of an advanced topic.

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 42 | 2 per week for 20 weeks and 2 in term 3 | 1 Hour | 42 | |

Problems Classes | 8 | Four in each of terms 1 and 2 | 1 Hour | 8 | |

Preparation and Reading | 150 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 3 Hours | 100% |

#### Formative Assessment:

Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University